When deploying Qt on Windows, you have to copy over a number of the dlls from the bin folder of the Qt directory.

On my system it is:

C:\Qt\4.8.4\bin

After you copy over all the required dll's from there, like QtCore4.dll and QtGui4.dll, if you are using any additional plugins like phonon or jpeg support, you need to copy those dll's over from the plugins folder:

C:\Qt\4.8.4\plugins

For example I make a folder in the folder with my exe called imageformats and I put qjpeg4.dll in that folder.

As far as Qwt works, you probably need to do a similar process to expose those dll's to your exe, and put them in the same folder as your exe.

The dll's listed above are for the "release" build of your exe. If you are running the "debug" version, it will look for <dll_name>d.dll.

The reasoning for putting in those paths has to do with the library search order that windows uses.